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A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho
A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho
Theses and Dissertations--Mathematics
Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases.
In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a …